\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}=2\times\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)

\(C=2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{15\times16}\right)\)

\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=2\times\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{3}{8}\)

c = 2/20 + 2/30 +2/42 + ... 2 /240

=2/4.5 +2/5.6 + 2/6.7 + ... +1/15.16

=2. (1/4.5 + 1/5.6 + 1/6.7 +...+1/15.16)

= 2.(1/4-1/5+1/5-...-1/16)

=2.(1/4-1/6)=2.3/16=3/8.

ghi nho dau cham la dau nhan

 Nhân cả TS và MS các phân số của tổng với 2 thì tổng không thay đổi và ta được:

                      2/20 + 2/30 + 2/42 + 2/56 + .... + 2/240

                   = 2/4x5 + 2/5x6 + 2/6x7 + 2/7x8 + ... + 2/15x16

                   = 2 x (1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ... + 1/15 - 1/16)

                   = 2 x (1/4 - 1/16)

                   = 2 x 3/16 = 3/8 

đúng rùi

tại sao bước thứ 4 ở trong ngoặc bạn lại lấy số đầu trừ số cuối?

1/10=2/20=2/(4.5)

1/15=2/30=2/(5.6)

1/21=2/42=2/(6.7)

....

1/120=2/240=2/(15.16)

=> C=1/10+1/15+...+1/120=2[1/(4.5)+1/(5.6)+...+1/(15.16)

       =2[1/4-1/16)=2(3/16)=3/8

nhân cả 2 vế với 2 ta có 

2C=1/20+1/30+1/42+....+1/240

2C=1/4X5+1/5X6+1/6X7+....+1/15X16

2C=1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16

2C=1/4-1/16 (khử liên tiếp)

2C=3/16

C=3/16:2

C=3/32

Cx2= (1/10+1/15+1/21+...+1/120)x2=2/20+2/30+2/42+.....+2/240=2/4x5+2/5x6+...+2/15x16=2x(1/4x5+1/5x6+.....+1/15x16)=2x(1/4-1/5+1/5-1/6+....+1/15-1/16)=2x(1/4-1/16)=2x(3/16)=0,375

=>C=0,375

Vậy C=0,375

\(C=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)

\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(C=\frac{2}{4\times5}+\frac{2}{5\times6}+\frac{2}{6\times7}+...+\frac{2}{15\times16}\)

\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(C=2\times\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(C=2\times\frac{3}{16}=\frac{3}{8}\)

\(C=\frac{2}{20}+\frac{2}{30}+.........+\frac{2}{240}\)

\(=2\left(\frac{1}{4.5}+\frac{1}{5.6}+..........+\frac{1}{15.16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.......+\frac{1}{15}-\frac{1}{16}\right)\)

\(=2\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(=2.\frac{3}{16}\)

\(=\frac{3}{8}\)

1/10+1/15+1/21+...+1/120

=2*(1/20+1/30+1/42+...+1/240)

=2*(1/4*5+1/5*6+...+1/15*16)

=2*(1/4-1/5+1/5-1/6+...+1/15-1/16)

=2*[(1/4-1/16)+(1/5-1.5)+...+(1/15-1/15)]

=2[(4/16-1/16)+0+...+0]]

=2*3/16=3/8

\(S=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)

\(S=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+....+\frac{2}{240}\)

\(2S=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\)

\(2S=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+.....+\frac{1}{15.16}\)

\(2S=\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)+.....+\left(\frac{1}{15}-\frac{1}{16}\right)\)

\(2S=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{15}-\frac{1}{16}\)

\(2S=\frac{1}{4}-\frac{1}{16}\)

\(2S=\frac{3}{16}\)

\(S=\frac{3}{8}\)

= 1 : 10 + 1 : 15 + 1 : 21 + ... + 1 : 120

= 1 : (10 + 15 + 21 + ... + 120)

= 1 : 670 = 1/670

 Đặt A = \(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\) 

=> A = \(2\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{240}\right)\)

        = \(2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)

        = \(2\left(\frac{1}{4}-\frac{1}{16}\right)=2\left(\frac{4}{16}-\frac{1}{16}\right)=2.\frac{3}{16}=\frac{3}{8}\)

Đặt A=1/10+1/15+1/21+...+1/120

    1/2 A=1/20+1/30+1/42+...+1/240

     A=1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16

     A=1/4-1/16

     A=3/16

Vậy:1/10+1/15+1/21+...+1/120=3/16

\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}=2\times\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)

\(C=2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{15\times16}\right)\)

\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=2\times\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{3}{8}\)

\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}=\frac{1}{2}x\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right):\frac{1}{2}\)

 = \(\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right):\frac{1}{2}=\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right):\frac{1}{2}\)

= \(\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{1}{16}\right):\frac{1}{2}=\frac{3}{8}\)

C= 1/10 + 1/15 + 1/21...........+1/120

C=1/10-1/120

C=11/12